{
  "arithmetic": "Python integers modulo 11; no NumPy or producer imports",
  "elapsed_seconds": 4.525,
  "independent_methods": {
    "hecke": "positive Merel matrices plus exact rational C_q boundary checks",
    "linear_algebra": "incremental sparse scalar elimination",
    "logarithms": "projection to the multiplicative subgroup of order 11",
    "modular_paths": "balanced Farey parents using modular inverses",
    "point_counts": "multiplicity table of y^2+y"
  },
  "linear_algebra": {
    "farey_generator_paths_checked_on_whole_quotient": 390,
    "hecke_constraint_rank": 63,
    "hecke_eigenspace_dimension": 2,
    "hecke_eigenvector_residuals_checked": 2730,
    "independent_point_counts": {
      "11": 16,
      "13": 17,
      "17": 24,
      "19": 15,
      "2": 5,
      "3": 6,
      "397": 374,
      "5": 9,
      "7": 13,
      "991": 1045
    },
    "manin_dimension": 65,
    "merel_matrix_counts": {
      "13": 63,
      "17": 93,
      "19": 109,
      "2": 4,
      "3": 7,
      "5": 15,
      "7": 25
    },
    "merel_right_coset_boundary_checks": {
      "13": 14,
      "17": 18,
      "19": 20,
      "2": 3,
      "3": 4,
      "5": 6,
      "7": 8
    },
    "normalization_index": 5,
    "normalization_value": 1,
    "plus_constraint_rank": 1,
    "plus_eigenspace_dimension": 1,
    "relation_rank": 325,
    "whole_quotient_hecke_comparisons": 177450
  },
  "schema": "kurihara-independent-verification-v1",
  "summation": {
    "all_csv_rows_independently_recomputed": true,
    "archival_literal_6_status": "NOT_REPRODUCED_NORMALIZATION_UNSPECIFIED",
    "block_count": 40,
    "csv_fields_checked": 1960200,
    "farey_word_edges_checked": 3493624,
    "modulus": 11,
    "n": 393427,
    "raw_product_sum": 43605160,
    "residue": 5,
    "sum_of_reduced_terms": 1437386,
    "unit_count": 392040
  },
  "verdict": "PASS"
}